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Escape Velocity

v=2GMrv = \sqrt{\frac{2GM}{r}}

Worked example: Earth surface escape → v = 11 186 m/s — press Try an example to run it live, then adjust anything.

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Constant used — built into this formula, no need to enter
G=6.6743×10−11 m3/(kg⋅s2)G = 6.6743 \times 10^{-11}\ \text{m}^{3}\text{/(kg}{\cdot}\text{s}^{2}\text{)}Newtonian constant of gravitation
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Grade 12Grade 12 Physics

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Escape Velocity explained

Mrv

Escape velocity comes from an energy balance: launch with kinetic energy ½mv² at least equal to the gravitational well's depth GMm/r, and the projectile coasts to infinity with nothing to spare. The projectile's own mass cancels, and the direction of launch doesn't matter — only the speed. For Earth, v = √(2 × 6.674 × 10⁻¹¹ × 5.97 × 10²⁴ / 6.371 × 10⁶) ≈ 11 190 m/s, the familiar 11.2 km/s that every Moon-bound Apollo mission had to approach.

Note the √2: escape speed is exactly √2 times circular orbital speed at the same radius. The formula also sorts the solar system's atmospheres — the Moon's gentle 2.4 km/s could not hold onto gas molecules, while Jupiter's crushing 59.5 km/s keeps even hydrogen. Push the logic to its limit by asking where escape velocity reaches the speed of light, and you arrive at the Schwarzschild radius of a black hole.

Escape Velocity formula

v=2GMrv = \sqrt{\frac{2GM}{r}}
Where
  • vv= Escape velocity (m/s)
  • MM= Central mass (kg)
  • rr= Starting distance (m)

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Part of this formula set

Gravitation and orbital mechanics

8 formulasNewton's inverse-square law and what falls out of it in orbit — field strength, orbital speed and period, Kepler's third law, and escape velocity.